Problem 12 - Algebra 1: Concepts and Skills

Question

Round to the nearest tenth. $$ 0.555 $$

Step-by-Step Solution

Answer

0.555 rounded to the nearest tenth is 0.6.

Step 1: Identify the Tenth's Place

First, recognize what number is in the tenth's place. The number 0.555 has a 5 in the tenth's place.

Step 2: Look to the Hundredth's Place

Next, examine the number in the hundredth's place. If this number is 5 or more, round up; if it is less than 5, round down. Here, the number is 5, so we will round up.

Step 3: Round to the Nearest Tenth

Finally, since we are rounding up, this means that 0.555 will be rounded to 0.6. So the nearest tenth to 0.555 is 0.6.

Key Concepts

Understanding Decimal Places

Decimals are numbers expressed using a decimal point to separate the whole number part from the fractional part. In the decimal number "0.555," each digit represents a fraction of a power of 10.
The first digit after the decimal point is the "tenth's place," the second is the "hundredth's place," and the third is the "thousandth's place."

• The tenth's place: This is the first digit after the decimal. In 0.555, it is the digit 5.
• The hundredth's place: This is the second digit after the decimal. In our number, it is also 5.
• The thousandth's place: This is the third digit after the decimal, in this case, also 5.

Understanding decimal places is crucial for accurately rounding numbers in mathematical calculations.

Rounding to the Nearest Tenth

Rounding a decimal to the nearest tenth means modifying the number to have only one digit after the decimal point. This process often simplifies calculations and makes numbers easier to interpret.
In the number 0.555, we look at the tenth's place, which is 5. Next, we check the digit in the hundredth's place. If it is 5 or more, we increase the digit in the tenth's place by one. If it is less than 5, the tenth's place remains the same. In this case, because the hundredth's place is also 5, we round up the tenth's place from 5 to 6.
Thus, 0.555 rounded to the nearest tenth becomes 0.6.

The Rounding Rules

Rounding follows a set of rules which make it easier to handle numbers in various situations like estimations or simplifying data. When rounding decimals, we primarily observe the digits immediately after the place you are rounding to:

• If the digit is 5 or greater, you "round up" by adding one to the digit you are rounding to.
• If the digit is less than 5, you "round down," which means you simply keep the digit you are rounding to as it is.

This method ensures that numbers are rounded in a way that balances out overestimations and underestimations across many uses. In our example of rounding 0.555 to the nearest tenth, the digit in the hundredth's place is 5, prompting us to round up and change 0.555 to 0.6.